Question

6. How do I tell the difference between an infinite solutions algebra problem or a one solution problem?7) 2x + 4 = x + x + 3+1

Answer 1

6) It has one solution 7) infinite solution

Step-by-step explanation:

3/4 (x-1) - 1/2 = 2(1-3x)

By expanding:

`\begin{gathered} \frac{3x\text{ -3}}{4}-\text{ }(1)/(2)=\text{ 2 - 6x} \\ \frac{3x\text{ -3 -2}}{4}=\text{ 2-6x cross multiply} \\ 3x\text{ -5 = 4(2-6x)} \\ 3x\text{ -5 = 8 -24x} \end{gathered}`

By collecting like terms:

`\begin{gathered} 3x\text{ + 24x = 8+ 5} \\ 27x\text{ = 13} \\ x\text{ = }(13)/(27) \end{gathered}`

To determine what category it belongs, we need to understand our variable (x) is equal to a value (13/27). When this happens, we say it has one solution.

7) 2x + 4 = x + x + 3+1

2x + 4 = 2x +4

2x-2x = 4-4

0 = 0

When we have the right side of the equation equal to the left side, then it has infinite number of solution.